vmbo kader and gt havo vwo
SOHCAHTOA calculator
Quick answer
sin(α) = opposite ÷ hypotenuse, cos(α) = adjacent ÷ hypotenuse, tan(α) = opposite ÷ adjacent.
Angle 30° and hypotenuse 10: opposite = 10 · sin(30°) = 5.
Calculator
Choose whether you are looking for sides or an angle. Fill in only what you know and leave the rest empty. Angles are in degrees. Answers use a decimal comma (4,70 rather than 4.70), the way Dutch schools and exams write numbers.
What is SOHCAHTOA?
SOHCAHTOA is a memory aid for the three trigonometric ratios in a right triangle: Sine = Opposite ÷ Hypotenuse, Cosine = Adjacent ÷ Hypotenuse, Tangent = Opposite ÷ Adjacent. Dutch classes say the same thing as SOS CAS TOA (S for schuine zijde, the hypotenuse), so both names appear in class.
To pick the right ratio, look at the angle and name the two sides in your problem: the one you know and the one you want. Opposite and hypotenuse means SOH. Adjacent and hypotenuse means CAH. No hypotenuse at all means TOA.
Looking for an angle? Work out the ratio first, then apply the inverse function: sin⁻¹, cos⁻¹ or tan⁻¹.
SOHCAHTOA only works in a right triangle. For other triangles havo B and vwo B use the sine rule or the cosine rule.
Examples by level
A 5 m ladder leans against a wall at an angle of 70° with the ground. How high up the wall does it reach?
- Which sides?The ladder is the hypotenuse (5 m). The height lies across from the 70° angle, so it is the opposite side.
- RatioOpposite and hypotenuse: SOH.
- Calculateopposite = 5 · sin(70°) = 4,70 m
The ladder reaches about 4,70 m up the wall.
A road rises 12 m over a horizontal distance of 80 m. What is the angle of the slope?
- Which sides?12 m lies across from the slope angle (opposite), 80 m lies along it (adjacent).
- Ratiotan(α) = opposite ÷ adjacent = 12 ÷ 80 = 0,15
- Inverseα = tan⁻¹(0,15) = 8,5°
The slope angle is about 8,5°.
In triangle ABC, angle C = 90°, angle A = 35° and AC = 9 cm. Find BC and AB.
- Sides from angle AAC touches angle A (adjacent), BC lies across from angle A (opposite), AB is the hypotenuse.
- BC with TOAopposite = 9 · tan(35°) = 6,30 cm
- AB with CAHhypotenuse = 9 ÷ cos(35°) = 10,99 cm
BC ≈ 6,30 cm and AB ≈ 10,99 cm. Check with Pythagoras: √(6,30² + 9²) ≈ 10,99.
Common mistakes
Wrong
Labelling opposite and adjacent once on the drawing and keeping those labels for every angle.
Right
Always look from the angle you are using. From the other acute angle, opposite and adjacent swap places.
Wrong
The calculator is in RAD (radians), so sin(30) does not give 0,5.
Right
Switch to DEG (degrees) and test it: sin(30) = 0,5.
Wrong
Getting sin(α) = 0,5 and writing that the angle is 0,5.
Right
0,5 is the ratio. The angle is sin⁻¹(0,5) = 30°.
Wrong
Using SOHCAHTOA in a triangle without a right angle.
Right
Find a right angle first, or draw an altitude so you get two right triangles.
Practice
vmbo Angle α = 40° and the opposite side is 6 cm. How long is the hypotenuse?
9,33 cm
Opposite and hypotenuse: SOH. hypotenuse = 6 ÷ sin(40°) = 9,33 cm.
havo The adjacent side is 6 and the hypotenuse is 10. Find angle α.
53,1°
cos(α) = 6 ÷ 10 = 0,6, so α = cos⁻¹(0,6) = 53,1°.
More practice, with an explanation for every mistake: SOHCAHTOA practice.
SOHCAHTOA on the Dutch exam
The 2027 central exam syllabus lists the same skill for wiskunde B havo (subdomain C1) and wiskunde B vwo (subdomain E1): using sine, cosine and tangent to calculate angles and side lengths in a right triangle.
For vmbo, the syllabus lists the ratios sine, cosine and tangent for the kader (kaderberoepsgericht) and gemengd/theoretisch tracks; in gemengd/theoretisch you also apply them in solids. The basis track does not include them.
When a question says “bereken” (calculate), the same syllabus asks for your working to show which steps you took. So write down which ratio you use and which numbers you substitute, not only the answer.
Next step
- How does this work? The explanation and examples are further up this page.
- See it visually SOHCAHTOA simulation: change the values and watch what happens.
- Test yourself SOHCAHTOA practice, with an explanation after every answer.
Learning path
- Learn first: Pythagorean theorem calculator Right triangle: a² + b² = c².
Frequently asked questions
What does SOHCAHTOA stand for?
Sine = Opposite ÷ Hypotenuse, Cosine = Adjacent ÷ Hypotenuse, Tangent = Opposite ÷ Adjacent. It only works in a right triangle. Dutch textbooks write the same rule as SOS CAS TOA.
Which side is opposite and which is adjacent?
It depends on the angle you are working with. The opposite side lies across from that angle, the adjacent side touches it. The hypotenuse is always the side across from the right angle.
How do you find an angle with sin, cos or tan?
Work out the ratio first, then use the inverse function. Opposite 5 and hypotenuse 10: sin(α) = 5 ÷ 10 = 0,5, so α = sin⁻¹(0,5) = 30°.
Why does my calculator give a strange answer?
It is probably set to radians (RAD) instead of degrees (DEG). For SOHCAHTOA at school you almost always work in degrees.